Why do I hear a rattling noise coming from the engine when I start the car? on 2003 Dodge Neon

Every time I start the car, the engine makes a rattling noise that really can be heard from inside the car. When I change it into reverse, the engine stops rattling.
When I open the hood and the car is in either Park or Drive, the rattling gets worse when I press down on the motor. If I pull up on the motor, the rattling noise goes almost away. When I drive and I am at at stop light or stop sign, the engine continues to rattle. Once the engine gets hot from driving around, the rattling noise coming from the engine goes away.
I checked the motor mounts, well at least I think I did and they looked ok.
I took it to the dealer and asked them how much a diagnostic would cost. I told that maybe the motor mounts may have to be changed. their estimate was at around 600 dollars...
Any ideas of what it could be?

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2 answers
i had a recent problem like that, all the same noises, i also checked the motor mounts and all that and everything was fine, the problem was just that my exhaust cover was rattling against my exhaust, and a quick bolt fixed it.
The dealer is probably right about the engine mounts but I would get another estimate, I see a five star rated repair shop on http://repairpal.com/directory Discount Car Care